'The total return on a portfolio of investments takes into account not only the capital appreciation on the portfolio, but also the income received on the portfolio. The income typically consists of interest, dividends, and securities lending fees. This contrasts with the price return, which takes into account only the capital gain on an investment.'

Which means for our asset as example:- The total return, or performance over 5 years of ProShares UltraPro QQQ is 97.5%, which is greater, thus better compared to the benchmark SPY (57.1%) in the same period.
- Looking at total return in of 11.8% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (32%).

'Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry.'

Using this definition on our asset we see for example:- Looking at the annual performance (CAGR) of 14.6% in the last 5 years of ProShares UltraPro QQQ, we see it is relatively greater, thus better in comparison to the benchmark SPY (9.5%)
- Compared with SPY (9.7%) in the period of the last 3 years, the compounded annual growth rate (CAGR) of 3.8% is lower, thus worse.

'Volatility is a rate at which the price of a security increases or decreases for a given set of returns. Volatility is measured by calculating the standard deviation of the annualized returns over a given period of time. It shows the range to which the price of a security may increase or decrease. Volatility measures the risk of a security. It is used in option pricing formula to gauge the fluctuations in the returns of the underlying assets. Volatility indicates the pricing behavior of the security and helps estimate the fluctuations that may happen in a short period of time.'

Which means for our asset as example:- Compared with the benchmark SPY (21.5%) in the period of the last 5 years, the historical 30 days volatility of 77.5% of ProShares UltraPro QQQ is larger, thus worse.
- Compared with SPY (17.9%) in the period of the last 3 years, the 30 days standard deviation of 71.7% is larger, thus worse.

'Risk measures typically quantify the downside risk, whereas the standard deviation (an example of a deviation risk measure) measures both the upside and downside risk. Specifically, downside risk in our definition is the semi-deviation, that is the standard deviation of all negative returns.'

Which means for our asset as example:- Looking at the downside risk of 55.5% in the last 5 years of ProShares UltraPro QQQ, we see it is relatively higher, thus worse in comparison to the benchmark SPY (15.5%)
- Compared with SPY (12.5%) in the period of the last 3 years, the downside deviation of 50.5% is larger, thus worse.

'The Sharpe ratio is the measure of risk-adjusted return of a financial portfolio. Sharpe ratio is a measure of excess portfolio return over the risk-free rate relative to its standard deviation. Normally, the 90-day Treasury bill rate is taken as the proxy for risk-free rate. A portfolio with a higher Sharpe ratio is considered superior relative to its peers. The measure was named after William F Sharpe, a Nobel laureate and professor of finance, emeritus at Stanford University.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.32) in the period of the last 5 years, the ratio of return and volatility (Sharpe) of 0.16 of ProShares UltraPro QQQ is lower, thus worse.
- Compared with SPY (0.41) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of 0.02 is lower, thus worse.

'The Sortino ratio improves upon the Sharpe ratio by isolating downside volatility from total volatility by dividing excess return by the downside deviation. The Sortino ratio is a variation of the Sharpe ratio that differentiates harmful volatility from total overall volatility by using the asset's standard deviation of negative asset returns, called downside deviation. The Sortino ratio takes the asset's return and subtracts the risk-free rate, and then divides that amount by the asset's downside deviation. The ratio was named after Frank A. Sortino.'

Applying this definition to our asset in some examples:- The ratio of annual return and downside deviation over 5 years of ProShares UltraPro QQQ is 0.22, which is lower, thus worse compared to the benchmark SPY (0.45) in the same period.
- Compared with SPY (0.58) in the period of the last 3 years, the excess return divided by the downside deviation of 0.03 is lower, thus worse.

'The Ulcer Index is a technical indicator that measures downside risk, in terms of both the depth and duration of price declines. The index increases in value as the price moves farther away from a recent high and falls as the price rises to new highs. The indicator is usually calculated over a 14-day period, with the Ulcer Index showing the percentage drawdown a trader can expect from the high over that period. The greater the value of the Ulcer Index, the longer it takes for a stock to get back to the former high.'

Which means for our asset as example:- The Ulcer Ratio over 5 years of ProShares UltraPro QQQ is 41 , which is larger, thus worse compared to the benchmark SPY (9.57 ) in the same period.
- During the last 3 years, the Ulcer Ratio is 49 , which is larger, thus worse than the value of 10 from the benchmark.

'Maximum drawdown is defined as the peak-to-trough decline of an investment during a specific period. It is usually quoted as a percentage of the peak value. The maximum drawdown can be calculated based on absolute returns, in order to identify strategies that suffer less during market downturns, such as low-volatility strategies. However, the maximum drawdown can also be calculated based on returns relative to a benchmark index, for identifying strategies that show steady outperformance over time.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum drop from peak to valley of -81.7 days of ProShares UltraPro QQQ is lower, thus worse.
- During the last 3 years, the maximum reduction from previous high is -81.7 days, which is smaller, thus worse than the value of -24.5 days from the benchmark.

'The Maximum Drawdown Duration is an extension of the Maximum Drawdown. However, this metric does not explain the drawdown in dollars or percentages, rather in days, weeks, or months. It is the length of time the account was in the Max Drawdown. A Max Drawdown measures a retrenchment from when an equity curve reaches a new high. It’s the maximum an account lost during that retrenchment. This method is applied because a valley can’t be measured until a new high occurs. Once the new high is reached, the percentage change from the old high to the bottom of the largest trough is recorded.'

Applying this definition to our asset in some examples:- Looking at the maximum days below previous high of 468 days in the last 5 years of ProShares UltraPro QQQ, we see it is relatively greater, thus worse in comparison to the benchmark SPY (439 days)
- During the last 3 years, the maximum time in days below previous high water mark is 468 days, which is larger, thus worse than the value of 439 days from the benchmark.

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Avg Drawdown Duration is the average amount of time an investment has seen between peaks (equity highs), or in other terms the average of time under water of all drawdowns. So in contrast to the Maximum duration it does not measure only one drawdown event but calculates the average of all.'

Applying this definition to our asset in some examples:- Looking at the average days under water of 136 days in the last 5 years of ProShares UltraPro QQQ, we see it is relatively greater, thus worse in comparison to the benchmark SPY (106 days)
- Compared with SPY (149 days) in the period of the last 3 years, the average days below previous high of 164 days is larger, thus worse.

Historical returns have been extended using synthetic data.
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- Note that yearly returns do not equal the sum of monthly returns due to compounding.
- Performance results of ProShares UltraPro QQQ are hypothetical, do not account for slippage, fees or taxes, and are based on backtesting, which has many inherent limitations, some of which are described in our Terms of Use.